/**
 * https://leetcode.com/problems/construct-the-rectangle/
 *
 * @author: wangjunchao(王俊超)
 * @time: 2019-07-10 09:59
 **/
public class Solution {
    /**
     * <pre>
     * For a web developer, it is very important to know how to design a web page's size.
     * So, given a specific rectangular web page’s area, your job by now is to design a
     * rectangular web page, whose length L and width W satisfy the following requirements:
     *
     * 1. The area of the rectangular web page you designed must equal to the given target area.
     *
     * 2. The width W should not be larger than the length L, which means L >= W.
     *
     * 3. The difference between length L and width W should be as small as possible.
     * You need to output the length L and the width W of the web page you designed in sequence.
     * Example:
     * Input: 4
     * Output: [2, 2]
     * Explanation: The target area is 4, and all the possible ways to construct it are
     * [1,4], [2,2], [4,1].
     * But according to requirement 2, [1,4] is illegal; according to requirement 3,  [4,1]
     * is not optimal compared to [2,2]. So the length L is 2, and the width W is 2.
     * Note:
     * The given area won't exceed 10,000,000 and is a positive integer
     * The web page's width and length you designed must be positive integers.
     * </pre>
     * @param area
     * @return
     */
    public int[] constructRectangle(int area) {
        if (area < 1) {
            throw new IllegalArgumentException("area: " + area);
        }

        int[] result = {0, 0};

        // 求平方根
        int width = (int) Math.sqrt(area);

        // width从平方根开始减少
        while (width > 0) {
            if (area % width == 0) {
                result[0] = area / width;
                result[1] = width;
                break;
            }

            width--;
        }

        return result;
    }
}
